In this work, we compare the finite sample performances of some prediction algorithms through simulation studies. We also want to see if the randomization is really beneficial in predicting binary sequences. Our study indicates that any sort of randomization is not really favorable for predicting almost all kind of binary data, hence the play-the-winner strategy is suggested. Our study also establishes some asymptotic results, in particular we characterize a sufficient condition for a prediction rule to be asymptotically optimal under the Markov chain scheme.